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3 years ago

Prove equal chords in the same circle subtend equal angles at circumference. Thank you!

1 answer:

7 0

Let AB and CD be two equal chords on the circumference. If you consider the triangles AOB and COD, where O is the center of the circumference, you have:

AO = CO, because they're both radii
BO = DO, for the same reason
AB=CD, given

So, the two triangles have the same side, and are congruent by the SSS theorem.

This implies that they also have the same angles, and in particular, the angles AOB and COD are the same.

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Multiply.

Nady [450]

$\boxed{3\sqrt{22}\sqrt{58}\sqrt{18}=18\sqrt{638}}$

<h2>Explanation:</h2>

Here we have the following expression:

$3\sqrt{22}\sqrt{58}\sqrt{18}$

So we need to simplify that radical expression. By property of radicals we know that:

$\sqrt[n]{a}\sqrt[n]{b}=\sqrt[n]{ab}$

So:

$3\sqrt{22}\sqrt{58}\sqrt{18}=3\sqrt{22\times 58 \times 18}=3\sqrt{22968}$

The prime factorization of 22968 is:

$22968=2^3\cdot 3^2\cdot11\cdot 29$

Hence:

$3\sqrt{22968}=3\sqrt{2^3\cdot 3^2\cdot11\cdot 29}=3\sqrt{2^2\cdot 3^2\cdot 2\cdot 11\cdot 29}$

By property:

$\sqrt[n]{a^n}=a$

So:

$3\sqrt{2^2\cdot 3^2\cdot 2\cdot 11\cdot 29} \\ \\ 3(2)(3)\sqrt{2\cdot 11\cdot 29}=18\sqrt{638}$

Finally:

$\boxed{3\sqrt{22}\sqrt{58}\sqrt{18}=18\sqrt{638}}$

<h2>Learn more:</h2>

Radical expressions: brainly.com/question/13452541

#LearnWithBrainly

3 0

3 years ago

What is the slope of the line perpendicular to the graph of 3x + 4y = 12?

WINSTONCH [101]

Answer:

${ \tt{slope = \frac{1}{3} }}$

Step-by-step explanation:

${ \tt{m _{1} \times m _{2} = - 1}} \\ { \tt{ - 3 \times m _{2} = - 1}} \\ { \tt{m _{2} = \frac{1}{3} }}$

7 0

3 years ago

Use your knowledge of the angle sum theorem to solve for x and find the missing angle of the triangle:

aev [14]

Answer:

x=20

Step-by-step explanation:

Well we know the right angle is 90 so...

And we also know that all the angle of a triangle add up to 180°.

Knowing this you can subtract 40° and 90°, this gives you 50°...

Then you can substitute 20° for x and then it will be 2(20°)+10°

Simplify and get 40°+10°

This equals 50° degrees

You then add that all up and you get 180°, this mean the answer is correct!

Hope this helps!

All the love, Ya boi Fraser :)

3 0

3 years ago

Read 2 more answers

Graph the inequlity <br> y > |x-7| + 1

Marysya12 [62]

Answer:

Step-by-step explanation:

The inequality graphed matches the graph on the answer choice D.

Hope this helps <3

5 0

2 years ago

15−2x=3x i need to find what x= but im stumped i have tried 6 and -6 but just cant get this

katrin [286]

X=3 because you have to isolate the variable by dividing each side by factors that don’t contain the variable .

3 0

4 years ago

Read 2 more answers